The Galactic Bar, the Kinematics of Nearby Stars in Gaia DR1, and Beyond Ortwin Gerhard Based on work with Matthieu Portail, Chris Wegg, Angeles Perez- Villegas (MPE), Melissa Ness (MPIA) 1. Overview: the barred Milky Way 2. Dynamical models for the Bulge-Bar: pattern speed, distribution of stellar and dark matter mass 3. Microlensing, IMF, Hercules 4. Chemo-Dynamics of different Bulge-Bar populations
The Milky Way Bar • Bulge looks like typical Box/Peanut bulge, as in external galaxies • Shape naturally similar to N-body simulations where the central part buckles into a B/P bulge leaving a thinner long bar outside • Based on RCG data from UKIDSS, VVV, 2MASS, with star-by-star extinction corrections B/P bulge and planar bar aligned, with bar angle 28-33 deg Estimated bar length 5.0±0.2 kpc, then corotation radius 6.0 kpc Shape of the bulge: Wegg & OG ‘13 Shape of long bar: Wegg, OG, Portail ‘15 Ortwin Gerhard, MPE Garching Lund, Auguet 2017 2
Bulge Kinematics & Metallicity • The BRAVA data for M-giant stars (L: Howard+ ’08, Kunder+’12) show nearly cylindrical rotation. • The cylindrical rotation is well fit by a boxy bulge formed from the disk. Simulations including a preexisting bulge of 8% ( 25%) of the disk (bulge) mass give sign. worse fit – most of the bulge made from the disk!? (L: Shen+’10 ) The near-cylindrical rotation is seen for all metallicities up to [Fe/H] -1 in the • ARGOS survey (R: Ness+ ’13). More metal-poor stars have higher dispersions. (also Babusiaux+ ’1 0, GIBS & GES surveys ( Zoccali+’17, Rojas - Arriagada+’17 ). Ortwin Gerhard, MPE Garching Lund, Auguet 2017 3
Overview: The Barred Milky Way Sun’s Distance to Gal. Centre: R0 = 8.2 kpc (±0.1) Circular velocity @ Sun V0 = 238 km/s (+5,-15) Solar motion wrt LSR (11.1, 12.4, 7.2) km/s Schoenrich+2010 Exponential disk scale-length Rd = 2.4 kpc (±0.5) inwards from the Sun Length of bar Rb = 5.0 kpc (± 0.2) Wegg, OG, Portail 2015 Corotation radius Rc = 6.1 kpc (±0.5) M bb = 1.9 10 10 Msun (± 0.1) Photom. bulge+bar Inner disk (<5.3 kpc) M id = 1.3 10 10 Msun (± 0.1) Portail, OG, Wegg, Ness 2017a Inner B+B+ID stellar mass fraction 65% Bulge stellar mass fraction 30% More discussion on structural parameters: Bland-Hawthorn+OG 2016 ARAA
Data Constraints for Bulge/Bar Dynamics + rotation . . Curve 3D density of RCGs Magnitude Proper motion Mean radial Mean radial velocities Distributions dispersion velocities and and dispersions as a dispersion function of distance These are (only) the data included by Portail, OG, Wegg, Ness 2017a • Star counts can be described by a density model. But stars move along their orbits. Therefore we need to combine with velocities. • Star counts and velocity data need to be described by a dynamical model. • Even though not strictly true, need to start with equilibrium dynamical model. NB: importance of accurate data (e.g., density). As for DF|M x,v, or , , • 5
Made-to-Measure Particle Method Need to fit many 1000s of observables (photometric, kinematics, population) in a rapidly rotating, complicated triaxial potential. Only currently practical way is with Made-to-Measure Particle (M2M) Models N-body model Model observable Real data “Observe” Compare & quantify Profit function Syer & Tremaine (1996), De Lorenzi+(2007), Change the particle weights Dehnen (2009), Portail+(2017a) Ortwin Gerhard, MPE Garching Lund, Auguet 2017 6
Some of the Data Fitted ARGOS: Observa- tional selection criteria ( Ness+’13 ) & mapping stars into distance bins using isochrones Wavy structure of v( ) shows streaming velocity field within the bar APOGEE predicted Portail, OG , Wegg, Ness 2017a Ortwin Gerhard, MPE Garching Lund, Auguet 2017 7
Bar Pattern Speed Good fits to kinematic observables for 35-42.5 km/s/kpc, depending slightly on M/N RCG . Joint χ 2 for ARGOS & BRAVA & syst. error estimate gives best value of pattern speed b =39±3.5 km/s/kpc Ω b influences bulge <v> and ; whereas mass in bulge region influences only . Independent measurement from future long bar kinematics. In good agreement with recent analysis of gas dynamics by Sormani+2015. With bar half-length R b =5.0±0.2 kpc find corotation radius R cr =6.1±0.5 kpc, R =1.2±0.1 Portail, OG, Wegg, Ness, 2017a Ortwin Gerhard, MPE Garching Lund, Auguet 2017 8
Result from Model Fit: Stellar Mass Structure Outer disk surface density meets bulge minor axis profile near end of bar; inner disk density nearly flat The models measure stellar masses in the inner 5 kpc of 1.9 10 10 M ⊙ in the bulge and bar , • 1.3 10 10 M ⊙ in the inner disk, • with typical error 0.1 10 10 M ⊙ 0.2 10 10 M ⊙ in the nuclear disk • ( 65% of total stellar mass) The total dynamical mass in the bulge WG13 volume is 1.85±0.05 10 10 M ⊙ (previously, 1.84 ± 0.07, Portail+’15) Portail, OG, Wegg, Ness 2017a, MNRAS Ortwin Gerhard, MPE Garching Lund, Auguet 2017 9
Dark Matter Density Profile Portail, OG, Wegg, Ness, 2017a • First dynamical evidence that the dark matter profile of the MW must have a core or shallow cusp: we know the total*, stellar, and hence the dark matter mass in the bulge, and that inside the radius of the Sun. The rotation curve wants it to be > NFW just inside the Sun, but then it must turn over. *Mb=(1.85±0.05) 10 10 M ⊙ • DM profile goes through local value from Piffl+’14 (not fitted), rises inwards, and flattens to a core or shallow cusp in the bulge region at 2 kpc. • Independently argued by Binney & Piffl ‘17 , from halo model fitted to local data, extrapolated to center, and using constraints from microlensing . Ortwin Gerhard, MPE Garching Lund, Auguet 2017 10
IMF from Microlensing Time-Scales • For individual lenses, ML time-scale is degenerate between lens mass, distance, transverse velocity. • But we now have dynamical models providing the statistical distribution of distances and transverse velocities • Also have ML time-scales of 3560 events from OGLE-III Wyrzykowski+’15 Thus can adjust IMF, hence present- day stellar mass function, to match Prefers near-Kroupa IMF very similar these time-scales using the model to local IMF, despite high- , old, • Assume a broken power-law IMF: rapidly formed stars in the inner MW Also prefers a low brown dwarf fraction Wegg et al. 2017 ApJL Ortwin Gerhard, MPE Garching Lund, Auguet 2017 11
IMF from Microlensing Time-Scales • For inidivual lenses, ML time-scale is degenerate between lens mass, distance, transverse velocity. • But we now have dynamical models providing the statistical distribution of distances and transverse velocities • Also have ML time-scales of 3560 events from OGLE-III Wyrzykowski+’15 Thus can adjust IMF, hence present- day stellar mass function, to match these time-scales using the model • Assume a broken power-law IMF: Prefers near-Kroupa IMF very similar to local IMF, despite high- , old, rapidly formed stars in the inner MW Also prefers a low brown dwarf Wegg et al. 2017 ApJL fraction Ortwin Gerhard, MPE Garching Lund, Auguet 2017 12
SNd: Revisiting the Hercules Stream So far, the Hercules stream in the SNd was identified with OLR orbits near the Sun; this is incompatible with Ωb=40 km/s/kpc when the OLR is at 11.5 kpc (Dehnen’00, Antoja+’14,Monari+’16) • Best model of P17a with increased resolution in the disk near Sun but no spiral arms • Cross-matched with Gaia TGAS-RAVE-LAMOST • Shows main bar-streaming component as well as low-V component consistent with (U,V) position of the Hercules stream Perez-Villegas et al 2017 Ortwin Gerhard, MPE Garching Lund, Auguet 2017 13
What Orbits Make Hercules in a Slow Bar • These are orbits circulating the L4 and L5 Lagrange points. Good fraction go to both L4 and L5 i.e. are stochastic. • They have long orbital periods in the rotating frame “Hercules goes to see the Galactic bar” Perez-Villegas et al 2017 Ortwin Gerhard, MPE Garching Lund, Auguet 2017 14
This model predicts that (i) Hercules stream fades outwards of the Sun (ii) Could be more prominent in the metal-rich stars (iii) Even the structure of the ‘gap’ with radius is not bad (NB: neither potential nor DF were made to match the disk though) Perez-Villegas et al 2017 Ortwin Gerhard, MPE Garching Lund, Auguet 2017 15
Chemo-Dynamical Bulge Models • Portail et al 2017b M2M particles carry [ x, v, f(M)] • MDF f(M) parameterized as MGE with indiv. Gaussians adjusted to ARGOS components • Particles projected into obsv space using isochrones and M-dependent selection fn • Particle metallicity weights w c adjusted by comparing with similar data in distance bins • The supersolar A bin has very pronounced bar ends. Contains younger stars? • B + A contribute roughly equal number of bar-supporting orbits. Stars in B have higher v, and could come from further out in the initial unstable disk Ness+’13, di Matteo+’14
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